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David Singmaster
David Breyer Singmaster (1939–) is a retired mathematics professor, formerly of the South Bank University in London, and a well-known figure in the recreational-mathematics scene and particularly in the Cube scene. His classic book Notes on Rubik's "Magic Cube", which was published from 1979 to 1981 and ran to five editions, introduced "Singmaster Notation" (which is now the standard) and also included one of the first published solutions. Cube-related publications * Notes on Rubik's "Magic Cube", David Singmaster. Enslow Publishers, 1981. * Handbook of Cubik Math, David Singmaster and Alexander H. Frey. The Lutterworth Press, 1982. * Rubik's Cubic Compendium, by Ernő Rubik and four others. Edited with an Introduction and Afterword by David Singmaster. Oxford University Press, 1987. * The Cube: The Ultimate Guide to the World's Bestselling Puzzle, Jerry Slocum, David Singmaster, Wei-Hwa Huang, Dieter Gebhardt, Geert Hellings, Ernő Rubik. Black Dog & Leventhal, 2009. Note that all the above Amazon links go to amazon.com (Amazon US); if yours is a different regional Amazon (e.g. amazon.co.uk), clicking on the link and then changing the .com to the country suffix of your country's Amazon will usually work. Singmaster's solution The Notes, as mentioned above, included one of the first published solutions, in the centre pages for easy reference. The following is how it appeared in the fifth (final) edition. It is a straightforward solution like many others; bottom layer first, them middle, then top. It is thus a forerunner of the Fridrich Method, which combines the first two layers into one step. As the Cube was a brand-new idea at the time, and speedcubing thus wasn't yet a thing, this solution was devised to be "memorable rather than efficient". 1: Form a cross (put U edges in place) # If the U edge you're trying to place is already in the U layer, but in the wrong position or orientation, turn the appropriate face to move it off the U layer. # If the UF edge is in D with the U facet facing downward, turn D until the edge is at DF, then do U2. # If the UF edge is in D with the F facet facing downward, turn D until the edge is at FD, then do F'U'RU. # If the UF edge is in the middle layer, rotate the U layer if need be until a quarter-turn would bring the piece into the UF position, then do this turn, and rotate the U face back to where it was. After doing the above once for every out-of-place U edge, you should have a cross (+) in the U face with its sides matching the colours of the side faces. 2: Put U corners in place Turn the cube so that the URF position needs a U corner to be placed in it. # If the required corner is somewhere else in U (including FUR or RFU), do a quarter-turn such that the corner is in D with the U facet not in D, do D2, then undo the quarter-turn. # Turn the D face until the URF corner is at DRF in some orientation. ## If URF is at FRD, apply D'R'DR. ## If URF is at RDF, apply DFD'F'. ## If URF is at DFR, apply FD2F'D2R'DR. Repeat until all four corners are placed; you should have a solid U face with all four sides agreeing with their centres. Now turn over the Cube so that the former U face is now D. 3: Place the middle layer edges Turn the cube so that an edge needs to be placed at FR. # If the required edge is already in the middle layer, turn the cube until the edge is in the FR position, then apply B'U (R2U2)3 U'B, which moves the edge to the BR position; then turn the cube back. # If the F facet of the FR edge is in U, turn U until the FR edge is at UL, then do LU (U2F2)3 U'L'. # If the R facet of FR is in U, turn U until the FR edge is at BU, then do B'U (R2U2)3 U'B. Repeat until the middle layer is solved. 4: Orient U edges Unless your Cube has been tampered with, or you made a mistake orienting edges in the previous steps, an even number (0, 2 or 4) of the U edges will be the right way up. If two edges need to be flipped, turn the cube until one of the two scenarios below is the case. # If you need to flip the edges at UL and UB, do BULU'L'B'. # If you need to flip UF and UB, do BLUL'U'B'. If you need to flip all four edges, do BLUL'U'B' Y2 BULU'L'B' 5: Place U edges If exactly two of the the U edges are in the correct places, turn U until 0, 1 or all 4 are correct (this will be either U or U'). Then: # If 1 is correct, turn the cube so it is at UL, and: ## If the other three need to be cycled clockwise (UF-UB-UR), do R2D'U2R'LF2RL'DR2. (Editor's Note: If you are interested only in solving the Cube, and not in speedsolving, you don't need an anticlockwise algorithm for this stage; if the anticlockwise case arises, do U2 Y' to turn it into the clockwise case.) ## If they need to be cycled anticlockwise, do R2DR'LF2RL'U2DR2. # If none are correct: ## If you need to do (UL-UB-UR-UF), do U. ## If you need to do (UL-UF-UR-UB), do U'. ## If you need to do (UF-UB) (UL-UR), do U2. ## If you need to do (UF-UR) (UL-UB), do R2D2B2D (L2F2)3 D'B2D2R2. 6: Place U corners # If three corners are wrongly placed, turn the cube until the one correct corner is at URF, then: ## If the others need to be cycled clockwise (UFL-BUL-BRU), do L'URU'R'LRUR'U'. ## If the others need to be cycled anticlockwise (UFL-BRU-BUL), do URU'R'L'RUR'U'L. # If adjacent corners need to be swapped, that is (UFL-FUR)(ULB-BRU), do B(LUL'U')3B'. # If opposite corners need to be swapped, that is (UFL-UBR)(ULB-RFU), do R'B2(FRF'R')3B2R. 7: Orient U corners # Turn the cube such that a corner which needs to be twisted is at URF, then: ## If it needs to be twisted clockwise, do (FDF'D')2. ## If it needs to be twisted anticlockwise, do (DFD'F')2. (Editor's Note: Unlike other monotwists, these ones don't need to be applied in opposing pairs; three monotwists in the same direction will work just as well.) # Turn just the U face until another unsolved corner is at URF, then do as above. Repeat until all corners are solved, then return the U layer to its rightful position, and you're done! See also * David Singmaster on Wikipedia. Category:People